Copy the .qrp files from the user directory (Inetpub\WWWRoot\MessageStatsReports\Reports\_Users\DomainName%5CUserName). You can also select to see subscriptions from all users when in the Subscription Site from the MessageStats Web Site.
There have been some issues that the user name doesn't change and the subscription stays under the old user profile in MessageStats Reports, but runs successfully when doing the following:
1. Open MessageStats Reports.
2. Click the File Icon on the top of the Exchange at a Glance Page and select Subscriptions.
3. Put a check mark in the Show subscriptions for all users at the bottom of the page beside the Configuration... button.
4. Click the desired Uses subscriptions to change the credentials for and select Modify, then walkthrough the steps.
5. When you get to Account, change the User Name and Password to the account.
6. Click Finish.
This will allow the subscription to be ran under the new credentials, but it won't transfer the actual subscription to be under another users profile in MessageStats Reports. You will have to select Show subscriptions for all users in order to view transferred subscriptions.
In MessageStats v6.0, an import and export for subscriptions has been included. When in the Subscriptions Site from the MessageStats Web Site, select the Subscriptions Menu and select to either import or export options.